To find the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex] for the function [tex]\( f(x) = 2x^2 + 1 \)[/tex], we will substitute [tex]\( x = 3 \)[/tex] into the function and simplify.
Given:
[tex]\[ f(x) = 2x^2 + 1 \][/tex]
Step-by-step solution:
1. Substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = 2(3)^2 + 1 \][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
3. Multiply by 2:
[tex]\[ 2 \times 9 = 18 \][/tex]
4. Add 1:
[tex]\[ 18 + 1 = 19 \][/tex]
Therefore, [tex]\( f(3) = 19 \)[/tex].
So the correct value of [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex] is [tex]\(\boxed{19}\)[/tex].
